Question

solve the equation 2x^2 + 14x + 9 =0

Answer 1

Answer:

$x = \bold{\frac{\sqrt{31} - 7}{2}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ OR \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \bold{\frac{-\sqrt{31} - 7}{2}}$

Step-by-step explanation:

$2x^2 + 14x + 9 = 0 \\ \\ 2x^2 + 14x = -9 \\ \\ = 2(x^2 + 7x) = -9 \\ \\ \\ x^2 + 7x = \frac{-9}{2} \\ \\ x^2 + 7x + 12\frac{1}{4} = \frac{-9}{2} + 12\frac{1}{4} \\ \\ = x^2 + 7x + \frac{49}{4} = \frac{-18}{4} + \frac{49}{4} \\ \\ = (x + \frac{7}{2})^2 = \frac{31}{4} \\ \\ \\ x + \frac{7}{2} = \frac{\sqrt{31}}{2} \\ \\ x = \bold{\frac{\sqrt{31} - 7}{2}} \\ \\ OR \\ \\ x + \frac{7}{2} = \frac{-\sqrt{31}}{2} \\ \\ x = \bold{\frac{-\sqrt{31} - 7}{2}}$